cos^4x + sin^4x=1/4(3+cos 4x)

Jawab

(cos⁴ x + sin⁴ x ) =  1/4 ( 3 + cos 4x)
cos⁴ x + sin⁴ x = (cos² x + sin²x)² - 2 sin² x cos² x
cos⁴ x + sin⁴ x = 1 - (2 sin x cos x) (sin x cos x)
cos⁴ x + sin⁴ x =1 - sin 2x ( 1/2 sin 2x)
cos⁴ x + sin⁴ x = 1 - 1/2 sin² 2x = 1/4 ( 4 - 2 sin² 2x)
cos⁴ x + sin⁴ x = 1/4 ( 4 +(cos 4x- 1))
cos⁴ x + sin⁴ x = 1/4 ( 3 + cos 4x)